Casati, Paolo
,
Terra machinis mota : dissertationes geometricae, mechanicae physicae hydrostaticae
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tam. </
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<
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>Sic autem inueſtigo ſuperficiem VY,
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quæ ſit media proportionalis inter differen
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tias illius & ſuperficiei vaſorum, hoc eſt in
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ter OM & CD. </
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C
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Ex datis
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duabus ſu
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perficiebus
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auferre ean
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dem ſuperfi
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ciem, quæ re
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linquat re
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sidua in Ra
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tione dupli
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cata data
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rum.
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<
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>Ratio ſuperficierum vaſorum ſit data 8
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ad 4; Ratio duplicata eſt 8. ad 2. Pono ſu
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perficiem ſolidi VY Algebricè 1℞. </
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>Quare ſu
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perficies aquæ OM eſt 8——1℞, & ſuperfi
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cies CD eſt 4——1℞: quæ ſunt inter ſe in du
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plicatâ Ratione ſuperficiei vaſorum: igitur
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8——1℞ ad 4——1℞. </
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>eſt vt 8 ad 2 ergo per
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19. 7. 16——2℞ æquatur 32——8℞. </
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ctâ Antitheſi æquatio demum eſt inter 16 &
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6℞. </
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>In ſtitutâ it aque diuiſione 1℞ eſt 2 2/3 ſuper
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ficies VY; quæ ablata ex 8 ſuperficie vaſis
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maioris relinquit ſuperficiem OM 5 1/3, &
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ablata ex ſuperficie vaſis minoris, hoc eſt ex
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4, relinquit ſuperficiem CD 1 1/3: eſt autem
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2 2/3 medio loco proportionalis inter 5 1/3 & 1 1/3,
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quæ præterea ſuperficies 5 1/3, & 1/3 ſunt in Ra
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tione duplicatâ Rationis 8 ad 4, hoc eſt in
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Ratione 8 ad 2. Iam verò ſi baſes aquarum
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OM ad CD ſint vt 8 ad 2, altitudines ve
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rò KN & GA reciprocè vt ſuperficies va
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ſorum, hoc eſt KN 4, & GA 8, erit aquą
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OMRS 32, & aqua CDFE 16, planè iņ
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Ratione, quam habent ſuperficies vaſorum,
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in quibus ipſæ aquæ exiſtunt. </
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